Finslerian and higher-order structure of space-time: Lie-invariance in fibres
In some recent papers [Rep. Math. Phys. 26, No.3, 367-399 (1988; Zbl 0691.53058)] the author proposed and investigated fibre-generalized gauge covariant field equations but did not include any Lie-invariance concepts. In this paper such an idea is taken into consideration assuming that each fibre has a Lie-group structure. The gauge fields are subject to conditions of Lie-invariance which ensure the Lie-invariance of the operator of covariant differentiation. Then by introducing the notion of a Lie-invariant field it is shown that all generalized gauge tensors are Lie-invariant. The homogeneous case is studied also. Assuming that all group structures in the fibres are isomorphic to each other, a kind of normal coordinates is introduced in order to simplify the calculations.
fibre-generalized gauge covariant field equations
scientific article; zbMATH DE number 4212915